Superconducting Transition Temperatures for Spin-Fluctuation Promoted Superconductivity in Heavy Fermion Compounds

TL;DR

This paper uses neutron scattering data and Eliashberg theory to calculate superconducting transition temperatures in heavy fermion compounds, linking AFM fluctuations to superconductivity.

Contribution

It provides a quantitative model connecting AFM fluctuation spectra to $T_c$ in heavy fermion superconductors, supporting AFM fluctuations as the pairing mechanism.

Findings

Calculated $T_c$ ratios match experimental data.

Superconductivity is likely caused by AFM fluctuations.

The model explains the normal state resistivity behavior.

Abstract

The quantum critical Antiferromagnetic (AFM) fluctuation spectra measured by inelastic neutron scattering recently in two heavy fermion superconductors are used together with their other measured properties to calculate their D-wave superconducting transition temperatures $T_{\rm c}$. To this end, the linearized Eliashberg equations for D-wave superconductivity induced by AFM fluctuations are solved in models of fermions with various levels of nesting. The results for the ratio of $T_{\rm c}$ to the characteristic spin-fluctuation energy are well parametrized by a dimensionless coupling constant and the AFM correlation length. Comparing the results with experiments suggests that one may reasonably conclude that superconductivity in these compounds is indeed caused by AFM fluctuations. This conclusion is strengthened by a calculation with the same parameters of the measured coefficient of the normal state quantum-critical resistivity $\propto T^{3/2}$ characteristic of {\it gaussian} AFM quantum-critical fluctuations. The calculations give details of the superconducting coupling as a function of the correlation length and the integrated fluctuation spectra useful in other compounds.